SOFIA, March 5 (Reuters) - Bulgarian miners, railway and coal-fired power plant workers marched through Sofia on Tuesday over possible job cuts, adding to a wave of demonstrations that have already felled the government.

Three people have set themselves on fire - two fatally - in mass protests against high electricity prices and low living standards, leaving Bulgaria facing an early election in May that will almost certainly leave a hung parliament.

The outgoing centre-right government announced March 6 as a day of national mourning after 36-year-old Plamen Goranov, who has become a symbol of the protests, died of his burns.

The miners are concerned that a rise in non-coal energy installation and public pressure to cut electricity prices may hurt coal-fired plants and mines and cause mass layoffs.

"We want to make sure that the thermal power plants work and buy the coal we produce. We are also citizens of this country, we too have the right to protest," said Borislav Ivanov, one of some 1,500 protesters who emptied sacks of coal outside the energy regulator's office.

Workers at state railway operator BDZ are concerned about jobs as the government seeks to sell off its cargo unit.

Rightist Prime Minister Boiko Borisov resigned last month after protests turned violent. His GERB party and the Socialists are neck-and-neck in opinion polls.

Neither looks likely to get an absolute majority and Borisov has indicated he will not work with any other grouping, suggesting an awkward coalition agreement or even an unworkable parliament that requires new elections.

While many people are frustrated with a political class they view as corrupt and doing little to improve living standards of less than half the European Union average, protesters have yet to unite behind a single leader or set of demands.

That could mean more votes for nationalist parties or the pro-business party of Meglena Kuneva, a former European commissioner who is relatively new to electoral politics.

DEMANDS

President Rosen Plevneliev is expected to appoint an interim government this week, saying it should address protesters demands' for stricter controls over electricity monopolies and maintain fiscal stability, which is important for confidence in a currency peg to the euro.

The energy regulator will rule later on Tuesday to cut electricity costs for households by an average of 7 percent, mainly at the expense of power distributors - Czech CEZ , Energo-Pro and EVN.

It said it would not exclude expensive power that comes from coal-fired plants from the electricity mix for households, as suggested by the outgoing energy minister, and tried to reassure miners that they have no reason to fear for their jobs.

Thermal power plants produce about 45 percent of the electricity in Bulgaria and the sector, including local mines, provide incomes to more than 50,000 people.

On Sunday, the state grid operator ordered the temporary closure of six units of three major coal-fired plants, due to a drop in domestic power consumption and exports.

Power exports dropped more than 20 percent last year due to falling demand and relatively high prices.

The opposition Socialists, who have criticised GERB's lax controls in the energy sector, demanded on Tuesday that the outgoing government stops the privatisation of the railways' cargo arm.

Four companies, including Romania's Grup Feroviar Roman, have been allowed to place bids by March 12. The proceeds, expected at about 100 million levs ($66.5 million), will be used to decrease BDZ's debt and secure a new loan from the World Bank. ($1 = 1.5034 Bulgarian levs) (Editing by Sam Cage and Robin Pomeroy)